Why is it some monks (Yuttadhammo specifically) walks barefoot in his alms rounds as well as while doing walking meditation?
Is there a purpose to it?
Barefoot used to be normal -- and wearing shoes was disrespectful and/or a sign of feeling superior.
The Vinaya used to explicitly allow footwear in outlying areas -- and not in public.
Lay society has changed, so wearing shoes is now seen as polite, and the custom has adapted accordingly -- i.e. you might see monks with footwear now - similarly there are times and places where the climate isn't appropriate for bare feet.
But I don't think of bare feet as remarkable. I used to walk barefoot as a teen (not for those same reasons), obviously enough it's feasible.
In ancient India , most of sages used to walk barefoot like tirthankar jains , buddha , their best students. Walking barefoot was also among poor locals. Nowdays too , few forest tribals of North-East India , Chhattisgarh & M.P. live barefoot.
Among sages , barefoot living was an indication to :
Simple life (like common man)
Vairagya (no interest in pleasures)
Energy tranfer occurs through foot
To not kill small beings ,even unwillingly(slight chance) cause barefoot increases sensations.
Truth-Seeker has stopped too much travelling and gone forth for deep meditation within a small area.
Moreover ,as Meditator becomes strong in meditation , tendency towards barefoot increases, without any enforcement of sheel(Vinaya) .
It is also very practical because one needs not dry out shoes or socks, going barefoot or wearing sandals of some kind solves this. The staying dry comes into play a lot as it gets cold andor wet, it takes a lot of maintenance and winter shoes are weighty.
Afaik people can comfortably walk thus partially exposed to cold even in low temperatures like -20C but it requires some conditioning.
Basically It solves the problem of having more requisites than one can carry, in particular the 2-3 pairs of footwear & socks. One is saving ~3kg of weight there which is a lot considering that it's probably going to make up for ~20% of the total weight of requisites which can be comfortably carried.